Intention polls - which are nowadays involved in most referendum and votes - have a well known feed-back effect on the very vote itself.

Indeed, a given citizen which has for instance made up his or her mind to choose the answer "A", as opposed to "B" in a given vote, is likely to feel (namely if the day to vote is a smart sunny one...) that it is useless to go to add his or her own small ballot paper to all the other one in favor of "A", as far as nevertheless, as asserted by a number of polls, "A" will win... Obviously, a collection of such a behavior is not really in favor of "A".

But effects linked to polls are sometimes much more complex than in this case, and could lead to complex collective responses. Let us take two examples to introduce such phenomenon :

● Some months ago, in the United States, a duel was opposing as usual Democrats and Republicans (Al Gore and Busch) for the succession of Clinton. The overall results of the ballots was, interestingly enough, a very accurate score, 50% ± e for the candidates (e being smaller than the usual errors rate..).

This score does not mean only that "a few more American are for Busch than for Al Gore". Its accuracy traduces rather something else, some implicit complex response of a large collectivity — at least the so called "floating voters" — to the simple choice at hand. It express namely, for many observers, something like neither Busch nor Al Gore are the host that American people dreams for the White House.

● In France, the results of a 1992 referendum on the amplification of the European Union (Maastricht) has been "yes". But it was a very small yes, with only 50%+e of ’yes’ answers. Such an e (<0.2) is an incredibly accurate score.

This score does not mean only that "there is a few more French people for Maastricht than against". Its accuracy traduces rather, here again, something else, some implicit complex response of a large collectivity (at least the so called "floating voters") to the simple choice at hand. It express namely, for many observers, something like not so happy with the European Union amplification, we are not for all that turning our back to Europe... In short, the collective response was a ’yes - but’... one.

How such accurate scores as the above ones can be achieved ? Let us present a theoretical approach which may provide a model of the involved mechanisms.

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II. A theoretical approach : the Specularity theory

Specularity theory was introduced by Jean-Louis Vullierme as a theoretical instrument for the macroscopic understanding of social morphogenesis.

Like more classical approaches, this theory views social forms as emerging from the underlying behavior of individuals. One of its specific features is yet to consider individual behavior as being determined by the model each individual has of how he or she should behave in a given situation.

This model is specular (i.e. mirror-like) in the following sense :

. the model an individual has of himself is also a model of the models other people have of him or her ;

. discrepancies between the model the individual has of himself and his or her model of the models other people have of him (and of themselves), are assessed in reference to the model the individual has (and other people have) of the model an independent and well-informed third party might have of such discrepancies.

Specular models are therefore :

(a) self-referential models of the modeling individual,

(b) models of the actual modeling activity of others,

and (c) models of the virtual modeling activity of neutral third parties appraising them both.

Individual models being cross-representations of models, and being submitted to a self-correcting mechanism (the virtual arbitration by third parties), they naturally tend to adjust. Social situations thus emerge from specular interaction between individuals forming such a network of "resonance" among them.

The very precise adjustment occurring in the scores of both the United States ballot and the French referendum could be accounted for by such specular interactions between networks of voters. This is indeed supported by a set of clues ; for instance, in France, until the last minute before voting for or against Maastricht, many people (including the authors of the paper) have not make up their mind, and were excitedly consulting polls, news-papers, weather, first estimations of the rate of voters, etc. before voting.

Such a behavior was obviously not directed to get any better understanding of the stake of the referendum ; it was more likely an (implicit) attempt to model the actual modeling activity of all others in the given situation, defining thus the model each individual has of how he or she should behave as regards the ballot. In such a framework, the overall accurate score emerges from specular interactions between individuals, adjusting a network of resonance around this score.